Explanation

From x = t → t = x  

Put in y = t² → y = x²  

So, x² = y

Explanation

If AB = BA, it means the matrices commute under multiplication.

So, they are called multiplicative commutative (or simply commutative) matrices.

Explanation

To complete the square for x⁴ + 64, recognize that:

(x²)² + 2(x²)(8) + 8² = (x² + 8)²

So, the missing term to complete the square is:

2(x²)(8) = 16x²

Explanation

Explanation

Given:  

x = t  

y = m

We are to find:  

(y − x)ⁿ = ?

Step-by-step:

1. Substitute the values of x and y into the expression:  

   (y − x)ⁿ = (m − t)ⁿ

Explanation

Given equation:

x² - 5x + 6 = 0

Factor the quadratic equation:

(x - 2)(x - 3) = 0

This gives us:

x - 2 = 0 or x - 3 = 0

x = 2 or x = 3

The roots of the equation are x = 2 and x = 3.

Explanation

x = √2 − 1  

x² = (√2 − 1)²  

= 2 − 2√2 + 1  

= 3 − 2√2

Explanation

Given:  

p(x) = x² - a·x² + 7

Combine like terms:  

p(x) = x²(1 - a) + 7

Now find p(2):  

p(2) = (2)²(1 - a) + 7  

= 4(1 - a) + 7  

= 4 - 4a + 7 = 11 - 4a

So, p(2) = 11 - 4a

Explanation

Matrix A =  

[ 5  6 ]  

[ 7  8 ]

To find the determinant of a 2×2 matrix:

det(A) = (5 × 8) - (6 × 7) = 40 - 42 = -2

Explanation

logₓ(16) = 2

This means:

x² = 16

Now take square root on both sides:

x = ±4

Since base of logarithm (x) must be positive and ≠ 1,  

x = 4 is the correct answer.